Constraint-Based Dynamics in the Panvitalistic Theory: Replacing the Lagrangian with Volume Invariance

The classical Lagrangian formalism $S = \int L \, dt$ is a cornerstone of standard physics but relies on an external time parameter and a continuum. The Panvitalistic Theory (PVT) eliminates both. This paper shows that the Lagrangian is an artefact of the historical dual time definition and replaces it with a volume-constraint operator derived directly from the axiom $\delta V = 0$. Dynamics emerge tautologically from rational 6D volume invariance and angular curvature ($\pi = T/L$). We introduce the clean notation $m$, $m_0$, $c_{\rm PVT}$, $E = L^6/T^5$ and demonstrate consistency with the Wheeler-DeWitt equation. PVT thereby provides a unified, rational, time-less dynamics without ad-hoc quantization.